Bayern, seventh in the standings after a rocky start, are already without Netherlands winger Arjen Robben, who aggravated a muscle injury at the World Cup in South Africa and could be sidelined until late this year.
French international Ribery was helped off the pitch in the 64th minute of Bayern's 2-1 league win at Hoffenheim on Tuesday after twisting his ankle just before Bayern's equaliser.
"He will not require surgery. That is good luck in his bad luck," said Bayern sports director Christian Nerlinger. "I believe he can begin training with the team in about three weeks."
"Obviously, Franck is a hugely important player for us. This is a setback for him but only a small one from which he can recover relatively quickly," Nerlinger said.
Ribery was injured while helping to end Bayern's Bundesliga goal drought stretching back to August 20, weaving his way into the area and seeing his curled drive palmed away by keeper Daniel Haas only for Thomas Muller to tuck away the rebound.
The 27-year-old will be in a cast for about 10 days and then wear a special shoe for another 10 days before he can start training.
"I am a bit relieved," said Bayern coach Louis van Gaal. "I feared far worse things had happened. Now I wish him a speedy recovery and to have him back in the team soon."
Bayern, who won their Champions League opener at home to AS Roma last week, visit Basel in their next Group E game on Tuesday.
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